Digital compression has become ubiquitous and has been used in a wide variety of applications (such as video and audio applications). When looking to image capture (i.e., photography) as an example, a image sensor (i.e., charged-coupled device or CCD) is employed to generate analog image data, and an ADC is used to convert this analog image to a digital representation. This type of digital representation (which is raw data) can consume a huge amount of storage space, so an algorithm is employed to compress the raw (digital) image into a more compact format (i.e., Joint Photographic Experts Group or JPEG). By performing the compression after the image has been captured and converted to a digital representation, energy (i.e., battery life) is wasted. This type of loss is true for nearly every application in which data compression is employed.
Compressive sensing is an emerging field that attempts to prevent the losses associated with data compression and improve efficiency overall. Compressive sensing looks to perform the compression before or during capture, before energy is wasted. To accomplish this, one should look to adjusting the theory under which the ADCs operate, since the majority of the losses are due to the data conversion. For ADCs to perform properly under conventional theories, the ADCs should sample at twice this highest rate of the analog input signal (i.e., audio signal), which is commonly referred to as the Shannon-Nyquist rate. Compressive sensing should allow for a sampling rate well-below the Shannon-Nyquist rate so long as the signal of interest is sparse in some arbitrary representing domain and sampled or sensed in a domain which is incoherent with respect to the representation domain.
Turning to FIG. 1, an example of a conventional CS-ADC 100 can be seen. As shown, a demodulator 103 (which is commonly referred to as a pseudorandom demodulator) smears an input signal (i.e., signal from amplifier 102) over a spectrum. This is generally accomplished by mixing a clock signal from a phase locked loop (PLL) 104 with sequences from sequencers 108-1 to 108-N (that are each coupled to memory 105 to receive a known sequence) by mixers 106-1 to 106-N. ADC pipeline 109-1 then uses an integrator 110-1 to 110-N (which functions as an anti-aliasing filter), a buffer 112-1 to 112-N, and a low rate Nyquist ADC 114-1 to 114-N. Effectively, the demodulator 103 creates nonuniform sampling intervals that appear to be random.
Some other conventional circuits are: U.S. Pat. No. 7,324,036; U.S. Pat. No. 7,834,795; Laska et al., “Theory and Implementation of an Analog-to-Information Converter Using Random Demodulation,” IEEE Intl. Symposium on Circuits and Systems, May 27-30, 2007, pp. 1959-1962; Meng et al., “Sampling Rate Reduction for 60 GHz UWB Communication Using Compressive Sensing,” Asilomar Conference on Signals, Systems & Computers, 2009; Benjamin Scott Boggess, “Compressive Sensing Using Random Demodulation” (Master's Thesis), 2009; Candes et al., “An Introduction to Compressive Sensing,” IEEE SP Magazine, March 2008; Tropp et al., “Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals”, IEEE Transactions on Information Theory, January 2010; and Chen et al., “A Sub-Nyquist Rate Sampling Receiver Exploiting Compressive Sensing”, IEEE Transactions on Circuits and Systemes-I, Reg. Papers, March 2011.